MUSIC OF THE SPHERES
The Orbits, Sizes, Rotations,
Velocities, and Trajectories of
our Local Planets and of our
Star
Chase Nordquist
The applications of Mathematics have allowed our contemporary scientists to
calculate and organize the physical properties of our celestial neighbors with great
precision. The following figures may have been unknown to our ancestors but the
importance of the paths and positions of objects in the sky were useful for knowing
when to sow and reap, or how they might influence character. Despite the shift,
these entities have perennially engendered awe and wonder.
SIZE
Diameter, Density, and mass
Sun:
Diameter (1.39 M km), Density (1.41 g/cm^3), Mass (1.989 E30 kg)
Mercury:
Diameter (4880 km), Density (5.43 g/cm^3), Mass (328.5 E21 kg)
Venus:
Diameter (12104 km), Density (5.24 g/cm^3), Mass (4.867 E24 kg)
Earth:
Diameter (12742 km), Density (5.51 g/cm^3), Mass (5.972 E24 kg)
Mars:
Diameter (6788 km), Density (3.92 g/cm^3), Mass (639 E21 kg)
Jupiter:
Diameter (139822), Density (1.33 g/cm^3), Mass (1.898 E27 kg)
Saturn:
Diameter (116464), Density (.69 g/cm^3), Mass (568.3 E24 kg)
Uranus:
Diameter (50724), Density (1.27 g/cm^3), Mass (86.81 E24 kg)
Neptune:
Diameter (49248), Density (1.64 g/cm^3), Mass (102.4 E24 kg)
Orbital Speed
Equatorial
Rotational Speed
Sun
7.189×103 km/h
Mercury
10.892 km/h
47.362 km/s
Venus
6.52 km/h
35.02 km/s
Earth
1,674.4 km/h
29.78 km/s
Mars
868.22 km/h
24.077 km/s
Jupiter
45,300 km/h
13.07 km/s
Saturn
35,500 km/h
9.69 km/s
Uranus
9,320 km/h
6.80 km/s
Neptune
9660 km/h
5.43 km/s
(relative to galactic center)
Velocity
220 km/s
ROTATIONS
Obliquity
Period of Equatorial Rotation
(perpendicular to ecliptic)
Sun:
7.25 ˚
(in Earth days/time)
25.6d
Mercury: 2.04 ˚
58.55d
Venus:
177.3 ˚
116.7d (retrograde spin)
Earth:
23.5 ˚
1d (24h)
Mars:
25 ˚
1d +40min
Jupiter:
3.13 ˚
9h +56min
Saturn:
26.7 ˚
10h +39min
Uranus
97.77 ˚
17h +14min
Neptune: 28.32 ˚
16h +16min
Obliquity (axis)
ORBITS AND TRAJECTORIES
(measured in 24 hour days)
Mercury
Venus
88 day year
225 day year
(measured in 24 hour days)
Earth
Mars
365.25 day year
687 day year
(measured in 24 hour days)
Jupiter
Saturn
4368 day year
10585 day year
(measured in 24 hour days)
Uranus
Neptune
30660 day year
60225 day year
Distances From Solar Center
Equations
for calculation of
periods of solar orbit
Kepler's
Equation for
approximating
planetary
trajectories
Contributing Equations
For expressing the velocity relative to
period:
:Escape Velocity
Retrieved from: http://astro.unl.edu/classaction/outlines/renaissance/slide1.html
Kepler's Laws of Planetary Motion
• The Kuiper Belt encircles our inner solar system
• Pluto is now described as a Kuiper Belt object
• The Kuiper is mostly comprised of ice an rock particles
• Renegade moons and planetoids may also exist in the belt
Other local features of interest
• The Oort Cloud encompasses
our entire solar system beyond
the Kuiper Belt
• It acts like a boundary of ice
and debris
Oort Cloud
Computer Model Aids and Sources
Universe Sandbox 3.0 for PC emulates programmable scenarios
Demonstration of Universe Sandbox 3.0 on personal computer
Sizes
http://exchange.smarttech.com/details?id=4b919913-ddb8-4297-bd37-f704782afce1
Speed
http://physicslens.com/page/2/
Speed chart
http://www.ritholtz.com/blog/2012/10/interactive-visualization-of-simultaneous-planet-orbits/orbit
Obliquity
http://www.astronoo.com/en/articles/axial-tilt-planets.html
Kepler Equation
http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
Mercury
http://songshuhui.net/archives/category/major/astro/page/8
Venus
http://astrobob.areavoices.com/2012/06/01/venus-speed-dates-mercury-en-route-to-transit/
Earth and Mars
http://www.sinequanonthebook.com/Gravity4.html
Jupiter
http://www.berkeley.edu/news/media/releases/2001/08/15_dippr.html
Saturn
http://www.slate.com/blogs/bad_astronomy/2009/03/17/incredible_quadruple_transit_on_saturn.htm
Urnaus
http://wisp.physics.wisc.edu/astro104/lecture24/lec24_print.html
Neptune
http://spaces.imperial.edu/russell.lavery/Ast100/Lectures/Ast100Topic12.html
(Sources for images in order of appearance)
Equations
http://www.slideshare.net/GregoryTewksbury/math-in-space-planetary-orbits
Kepler’s laws
http://astro.unl.edu/classaction/outlines/renaissance/slide1.html
Oort cloud
http://wagner.edu/hawktalk/goddards-testing-facilities-where-we-build-satellites-then-try-to-break-them/
Kuiper belt
http://astronomie-handeloh.de/projekte/planeten/pluto.htm
Computer Models
http://www.codeincodeblock.com/2012/06/3d-solar-system-simulation-graphics.html
Universe Sandbox
http://www.jasonloch.net/2011/06/universe-sandbox/
(sources continued)
“Music of the spheres“
by chase Nordquist
sp2015